The present invention relates to an image reconstruction algorithm for magnetic resonance imaging(MRI). More particularly, this invention is concerned with a high-resolution image reconstruction method for MRI that improves resolution under a given gradient field strength.
Current main streams of image reconstruction methods for MRI include an n-dimensional (n=2, 3, . . . ) Fourier transformation method, and a back projection method that corresponds to polar coordinate expression of the Fourier transformation. These methods are all based on Fourier transformation.
According to the Nyquist's theorem, a frequency resolution .DELTA.f.sub.O =1/T.sub.x is attained during an observation time T.sub.x .multidot.A "Nyquist spatial resolution" .DELTA.X.sub.O corresponding to the frequency resolution .DELTA.f.sub.O is calculated using a gradient field strength G.sub.x [T/m]. When a Larmor constant .gamma. is used to demonstrate the relation between the resolutions, EQU 1/T.sub.x =(.gamma..multidot.G.sub.x /2.pi.).multidot..DELTA.X.sub.O
is provided. T.sub.x =N.multidot..DELTA.t is assigned to this expression. Then, when the resultant expression is simplified, EQU .gamma..multidot.G.sub.x .multidot..DELTA.X.sub.O .multidot..DELTA.t=2.pi./N
is provided, which is referred to as a "Nyquist condition".
To increase a spatial resolution .DELTA.X under the Nyquist conditions, a G.sub.x or T.sub.x value, and a size of an applied gradient field (product of strength G.sub.x by time T.sub.x) must be increased. However, a gradient field strength applicable during a given echo time TE has a limit specific to individual hardware.
Therefore, when a discrete Fourier transformation(DFT) reconstruction algorithm based on an orthogonal transformation is adopted, if an attempt is made to improve resolution, a gradient coil, a power supply, and other hardware must be renovated to increase the gradient field strength (the resolution will improve in proportion to the gradient field strength). No other means is available.